Testing the Lorentz Invariance of Light with a Birefringent Cavity

We report on the progress of a novel experimental test of the isotropy of $c$, based on measuring the birefringence of a single optical cavity. Tests of the isotropy of $c$ typically compare the phase velocities of two orthogonally propagating optical modes. Using pairs of high-finesse optical cavities, such tests have constrained direction-dependent variations in the speed of light to the level of parts per $10^{17}$ [1-2]. The precision of these tests is presently limited by systematic stochastic fluctuations in the relative length of such cavities. We have developed an experiment which compares the phase velocities of two orthogonally polarized optical modes in a single high-finesse dielectric-filled optical cavity. Since anisotropies in $c$ can make otherwise isotropic materials optically birefringent [3-4], we anticipate that we will be able to place significantly tighter constraints on Lorentz violation for photons. \\[4pt] [1] S. Herrmann, A. Senger, K. M\"ohle, M. Nagel, E.V. Kovalchuk and A. Peters, PRD 80, 105011 (2009).\newline [2] Ch. Eisel, A. Yu. Nevsky, and S. Schiller, PRL 103, 090401 (2009).\newline [3] H. M\"uller, PRD 71, 045004 (2005).\newline [4] V.A. Kosteleck\'y and M. Mewes, PRD 80, 015020 (2009).